Merchies also have a line over the side while at anchor. The Merchies have a lifering tied to the line, to help the person in the water have something larger than the line to grab hold of.

I've never seen it dragged while the vessel was u/w but I can think of many reasons why that would be fruitless in any situation.
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QMC, USCG (Ret)
The best luck is what you make yourself!